As for what superhero characters might still be published in the 22nd, 23rd, and 24th centuries, the only one I think would still be published is.....Superman.
Why only Superman? Well, his fight spans centuries, as seen in a few stories (in particular one 1965 story about 'Klar Ken'), so it's possible that a version of Kal-El could exist in those centuries. Batman....I don't think so, his mission/fight only works in a 20th/21st century context of American cities having the paticular kind of crime it did/does now that contributed to his parent's deaths and to him becoming Batman (maybe it could work in the context of a space colony [that failed] similar to Turxakana IV.) Wonder Woman could be retconned as being from another planet (or dimension) who decides to safeguard the universe and Earth despite it being what it is. The Flash and a ton of others. Somebody in those centuries would have to figure where they would fit in a future society like that of the UER (United Earth Republic) and UPP (perhaps the Legion of Super Heroes can be set up and work as published adventures somehow.)